Simplify the following expression: $y = \dfrac{-54n^3 + 54n^2}{81n^3 + 9n^2}$ You can assume $n \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-54n^3 + 54n^2 = - (2\cdot3\cdot3\cdot3 \cdot n \cdot n \cdot n) + (2\cdot3\cdot3\cdot3 \cdot n \cdot n)$ The denominator can be factored: $81n^3 + 9n^2 = (3\cdot3\cdot3\cdot3 \cdot n \cdot n \cdot n) + (3\cdot3 \cdot n \cdot n)$ The greatest common factor of all the terms is $9n^2$ Factoring out $9n^2$ gives us: $y = \dfrac{(9n^2)(-6n + 6)}{(9n^2)(9n + 1)}$ Dividing both the numerator and denominator by $9n^2$ gives: $y = \dfrac{-6n + 6}{9n + 1}$